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Institute for Applied and Numerical Mathematics
Junior Research Group: Numerics of PDEs
JProf. Dr. Roland Maier
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JProf. Dr. Roland Maier

  • Karlsruhe Institute of Technology (KIT)
    Institute for Applied and Numerical Mathematics
    Englerstr. 2
    76131 Karlsruhe
    Germany

Welcome on my webpage. Since July 2023, I am junior professor at the Institute for Applied and Numerical Mathematics and leader of the junior research group Numerics of PDEs. Moreover, I am member of the Collaborative Research Center 1173 Wave Phenomena and PI of the project A15. I mainly work on numerical homogenization methods for multiscale problems and on specifically designed time stepping techniques for coupled PDEs. Moreover, I am very interested in the combination of machine learning techniques and classical numerical methods.

In the summer term 2025, I will give the lecture Analytical and Numerical Homogenization. The lecture gives an introduction into special methods to efficiently treat multiscale phenomena. Moreover, I will offer a seminar on special topics in the context of the finite element method. In the winter term 2025/26, I will once again give the lecture Numerical Analysis of Neural Networks.

If you are interested in writing a Bachelor or Master thesis in the area of Numerical Mathematics, feel free to talk to me or write me an informal email.

Current List of Courses
Semester Titel Typ
Summer Semester 2025 Analytical and Numerical Homogenization Lecture
Selected Topics on Finite Elements Seminar
Winter Semester 2024/25 Finite Element Methods Lecture
Summer Semester 2024 Numerical Analysis of Neural Networks Lecture
Winter Semester 2023/24 Analytical and Numerical Homogenization Lecture
Ringvorlesung Wavephenomena Lecture

Upcoming Events

Research Interests

  • Multiscale Methods
  • Numerical Homogenization
  • Semi-explicit methods for coupled PDEs
  • Discretization of (time-dependent) PDEs

Short CV

  • since JUL 2023: Junior Professor for Numerics of Partial Differential Equations, Karlsruhe Institute of Technology
  • OCT 2021 - JUN 2023: Junior Professor for Numerical Analysis, Friedrich Schiller University Jena, Germany
  • SEP 2020 - SEP 2021: PostDoc, Chalmers University of Technology and University of Gothenburg, Sweden
  • APR 2020 - AUG 2020: PostDoc, University of Augsburg, Germany
  • APR 2017 - MAR 2020: Doctoral student, University of Augsburg, Germany
  • SEP 2012 - MAR 2017: Bachelor and Master studies, University of Bonn, Germany

Awards and Prizes

  • Winner of the ECCOMAS PhD Olympiad 2021
  • Dr.-Klaus-Körper prize of the GAMM 2021
  • Kulturpreis Bayern 2020, dissertation prize
  • Appointed member of the GAMM Juniors (2020-2022)

Publications

Submitted Articles

  1. M. Elasmi, F. Krumbiegel, and R. Maier. Neural numerical homogenization based on deep Ritz corrections. ArXiv Preprint, 2024.
  2. Z.-S. Liu, R. Maier, and A. Rupp. Numerical homogenization by continuous super-resolution. ArXiv Preprint, 2024.
  3. M. Hauck, R. Maier, and A. Målqvist. An algebraic multiscale method for spatial network models. ArXiv Preprint, 2023.
  4. P. Lu, R. Maier, and A. Rupp. A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods. ArXiv Preprint, 2023.

Refereed Articles

  1. F. Krumbiegel and R. Maier. A higher-order multiscale method for the wave equation. Accepted for publication in IMA J. Numer. Anal., 2024.
  2. D. Gallistl and R. Maier. Localized implicit time stepping for the wave equation. SIAM J. Numer. Anal., 62(4):1589-1608, 2024.
  3. R. Altmann, R. Maier, and B. Unger. Semi-explicit integration of second order for weakly coupled poroelasticity. BIT Numer. Math., 64, Article No. 20, 2024.
  4. F. Kröpfl, R. Maier, and D. Peterseim. Neural network approximation of coarse-scale surrogates in numerical homogenization. Multiscale Model. Simul., 21(4):1457-1485, 2023.
  5. Z. Dong, M. Hauck, and R. Maier. An improved high-order method for elliptic multiscale problems. SIAM J. Numer. Anal., 61(4):1918-1937, 2023.
  6. S. Geevers and R. Maier. Fast mass lumped multiscale wave propagation modelling. IMA J. Numer. Anal., 43(1):44-72, 2023.
  7. R. Maier, P. Morgenstern, and T. Takacs. Adaptive refinement for unstructured T-splines with linear complexity. Comput. Aided Geom. Design, 96:102117, 2022.
  8. F. Kröpfl, R. Maier, and D. Peterseim. Operator compression with deep neural networks. Adv. Cont. Discr. Mod., 2022, Paper No. 29, 2022.
  9. P. Ljung, R. Maier, and A. Målqvist. A space-time multiscale method for parabolic problems. Multiscale Model. Simul., 20(2):714-740, 2022.
  10. R. Maier and B. Verfürth. Multiscale scattering in nonlinear Kerr-type media. Math. Comp., 91(336):1655-1685, 2022.
  11. R. Altmann and R. Maier. A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability. SIAM J. Sci. Comput., 44(3):B457-B478, 2022.
  12. R. Maier. A high-order approach to elliptic multiscale problems with general unstructured coefficients. SIAM J. Numer. Anal., 59(2):1067-1089, 2021.
  13. R. Altmann, R. Maier, and B. Unger. Semi-explicit discretization schemes for weakly-coupled elliptic-parabolic problems. Math. Comp., 90(329):1089-1118, 2021.
  14. A. Caiazzo, R. Maier, and D. Peterseim. Reconstruction of quasi-local numerical effective models from low-resolution measurements. J. Sci. Comput., 85(1), Article No. 10, 2020.
  15. R. Altmann, E. Chung, R. Maier, D. Peterseim, and S.-M. Pun. Computational multiscale methods for linear heterogeneous poroelasticity. J. Comput. Math., 38(1):41-57, 2020.
  16. P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, and M. Kästner. A diffuse modeling approach for embedded interfaces in linear elasticity. GAMM-Mitteilungen, 43(1):e202000001, 2020.
  17. S. Fu, R. Altmann, E. Chung, R. Maier, D. Peterseim, and S.-M. Pun. Computational multiscale methods for linear poroelasticity with high contrast. J. Comput. Phys., 395:286-297, 2019.
  18. R. Maier and D. Peterseim. Explicit computational wave propagation in micro-heterogeneous media. BIT Numer. Math., 59(2):443-462, 2019.
  19. C. Paulus, R. Maier, D. Peterseim, and S. Cotin. An immersed boundary method for detail-preserving soft tissue simulation from medical images. In: P. Nielsen, A. Wittek, K. Miller, B. Doyle, G. Joldes, and M. Nash, editors, Computational Biomechanics for Medicine, MICCAI 2017, pp. 55-67. Springer, Cham, 2019.

Articles in Collections

  1. P. Hennig, M. Kästner, R. Maier, P. Morgenstern, and D. Peterseim. Adaptive isogeometric phase-field modeling of weak and strong discontinuities. In: J. Schröder and P. Wriggers, editors, Non-standard Discretisation Methods in Solid Mechanics, volume 98 of Lecture Notes in Applied and Computational Mechanics, pp. 243-282. Springer, Cham, 2022.

Articles in Proceedings

  1. R. Altmann, R. Maier, and B. Unger. A semi-explicit integration scheme for weakly-coupled poroelasticity with nonlinear permeability. Proc. Appl. Math. Mech., 20(1):e202000061, 2021.
  2. A. Caiazzo, R. Maier, and D. Peterseim. Reconstruction of quasi-local numerical effective models from low-resolution measurements. Oberwolfach Reports, 16(3):2149-2152, 2019.
  3. R. Maier and D. Peterseim. Fast time-explicit micro-heterogeneous wave propagation. Proc. Appl. Math. Mech., 18(1):e201800294, 2018.

Theses

  1. R. Maier. Computational Multiscale Methods in Unstructured Heterogeneous Media. Doctoral Thesis, University of Augsburg, 2020.
  2. R. Maier. Simulation of Elastic Deformation by the Immersed Boundary Method. Master Thesis, University of Bonn, 2017.
  3. R. Maier. Die Space-Time-DG-Methode: Theorie und Numerik für parabolische Gleichungen in einer Dimension. Bachelor Thesis, University of Bonn, 2015. In German.